Cats & Dogs #284: 10x10 Grid Puzzle (Hard)

Step-by-step solution

Squares are written as R<row>C<column>, counting from the top-left.

1. The = clue between R1C7 and R1C6 means they are the same. R1C7 is a dog, so R1C6 is a dog.
2. The = clue between R8C4 and R9C4 means they are the same. R8C4 is a dog, so R9C4 is a dog.
3. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
4. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
5. R8C4 and R9C4 are both dogs, so R7C4 must be a cat (no three in a row).
6. R8C4 and R9C4 are both dogs, so R10C4 must be a cat (no three in a row).
7. R7C8 and R9C8 are both cats with one square between them, so R8C8 must be a dog.
8. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
9. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
10. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
11. Column 8 already has its 5 cats, so R5C8 and R6C8 must be dogs.
12. The × clue between R6C8 and R6C7 means they are different. R6C8 is a dog, so R6C7 is a cat.
13. Imagine R10C2 were a cat: following the rules from there soon forces a contradiction, so R10C2 must be a dog.
14. The = clue between R10C2 and R10C3 means they are the same. R10C2 is a dog, so R10C3 is a dog.
15. R10C2 and R10C3 are both dogs, so R10C1 must be a cat (no three in a row).
16. R8C1 and R10C1 are both cats with one square between them, so R9C1 must be a dog.
17. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
18. The = clue between R2C3 and R2C4 means they are the same. R2C3 is a cat, so R2C4 is a cat.
19. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
20. The × clue between R2C2 and R3C2 means they are different. R2C2 is a dog, so R3C2 is a cat.
21. The × clue between R3C2 and R4C2 means they are different. R3C2 is a cat, so R4C2 is a dog.
22. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
23. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
24. Imagine R3C3 were a cat: following the rules from there soon forces a contradiction, so R3C3 must be a dog.
25. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
26. The = clue between R3C4 and R3C5 means they are the same. R3C4 is a cat, so R3C5 is a cat.
27. R3C4 and R3C5 are both cats, so R3C6 must be a dog (no three in a row).
28. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
29. The = clue between R3C7 and R4C7 means they are the same. R3C7 is a cat, so R4C7 is a cat.
30. R4C7 and R4C8 are both cats, so R4C6 must be a dog (no three in a row).
31. R4C7 and R4C8 are both cats, so R4C9 must be a dog (no three in a row).
32. R2C4 and R3C4 are both cats, so R4C4 must be a dog (no three in a row).
33. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
34. R4C4 and R4C6 are both dogs with one square between them, so R4C5 must be a cat.
35. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
36. R1C6 and R3C6 are both dogs with one square between them, so R2C6 must be a cat.
37. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
38. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
39. R2C7 and R2C8 are both dogs, so R2C9 must be a cat (no three in a row).
40. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
41. R5C7 and R5C8 are both dogs, so R5C9 must be a cat (no three in a row).
42. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
43. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
44. The = clue between R4C1 and R5C1 means they are the same. R4C1 is a cat, so R5C1 is a cat.
45. The = clue between R5C1 and R5C2 means they are the same. R5C1 is a cat, so R5C2 is a cat.
46. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
47. R5C3 and R5C5 are both dogs with one square between them, so R5C4 must be a cat.
48. R4C1 and R5C1 are both cats, so R6C1 must be a dog (no three in a row).
49. R5C3 and R7C3 are both dogs with one square between them, so R6C3 must be a cat.
50. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
51. The × clue between R6C4 and R6C5 means they are different. R6C4 is a dog, so R6C5 is a cat.
52. R6C5 and R6C7 are both cats with one square between them, so R6C6 must be a dog.
53. Row 4 already has its 5 cats, so R4C10 must be dogs.
54. Row 5 already has its 5 cats, so R5C10 must be dogs.
55. R4C10 and R5C10 are both dogs, so R3C10 must be a cat (no three in a row).
56. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
57. Row 3 already has its 5 cats, so R3C9 must be dogs.
58. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
59. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
60. R1C1 and R3C1 are both dogs with one square between them, so R2C1 must be a cat.
61. Row 2 already has its 5 cats, so R2C10 must be dogs.
62. Column 1 already has its 5 cats, so R7C1 must be dogs.
63. R7C1 and R7C3 are both dogs with one square between them, so R7C2 must be a cat.
64. R5C2 and R7C2 are both cats with one square between them, so R6C2 must be a dog.
65. Row 6 already has its 5 dogs, so R6C9 must be cats.
66. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
67. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
68. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
69. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
70. R7C6 and R7C8 are both cats with one square between them, so R7C7 must be a dog.
71. Row 7 already has its 5 dogs, so R7C10 must be cats.
72. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
73. R8C8 and R8C10 are both dogs with one square between them, so R8C9 must be a cat.
74. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
75. R1C8 and R1C9 are both cats, so R1C10 must be a dog (no three in a row).
76. Column 9 already has its 5 cats, so R9C9 must be dogs.
77. Column 10 already has its 5 dogs, so R9C10 and R10C10 must be cats.
78. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
79. R8C2 and R8C4 are both dogs with one square between them, so R8C3 must be a cat.
80. R8C2 and R10C2 are both dogs with one square between them, so R9C2 must be a cat.
81. The × clue between R9C2 and R9C3 means they are different. R9C2 is a cat, so R9C3 is a dog.
82. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).
83. Column 5 already has its 5 cats, so R8C5 must be dogs.
84. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
85. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
86. Row 8 already has its 5 dogs, so R8C7 must be cats.
87. Row 9 already has its 5 dogs, so R9C7 must be cats.
88. R8C7 and R9C7 are both cats, so R10C7 must be a dog (no three in a row).
89. Column 5 already has its 5 cats, so R10C5 must be dogs.
90. R10C5 and R10C7 are both dogs with one square between them, so R10C6 must be a cat.